What do the entries in Lamport clocks representations represent?

Question

I'm trying to understand an illustrative example of how Lamport's algorithm is applied. In the course that I'm taking, we were presented with two representations of the clocks within three [distant] processes, one with the lamport alogrithm applied and the other without.

Without the Lamport algorithm:

With the lamport algorithm applied:

My question is concerning the validity of the change that was applied to the third entry of the table pertaining to the process P1. Shouldn't it be, as the Lamport algorithm instructs, max(2, 2) + 1, which is 3 not 4?

When I asked some of my classmates regarding this issue, one of them informed me that the third entry of the table of P1 represents a "local" event that happened within P1, and so when message A is arrived, the entry is updated to max(2, 3) + 1, which is 4. However, if that was the case, shouldn't the receipt of the message be represented in a new entry of its own, instead of being put in the same entry that represents the local event that happened within P1?

Upon further investigation, I found, in the same material of the course, a figure that was taken from Tannenbaum's Distributed Systems: Principles and Paradigms , in which the new values of an entry that corresponds to the receipt of a message is updated by adding 1 to the max of the entry before it in the same table and the timestamp of the received message, as shown below, which is quite different from what was performed in the first illustration.

I'm unsure if the problem relates to a faulty understanding that I have regarding the algorithm, or to the possibility that the two illustrations are using different conventions with respect to what the entries represent.

Answer 1

validity of the change that was applied to the third entry of the table pertaining to the process P1

In classical lamport algorithm, there is no need to increase local counter before taking max. If you do that, that still works, but seems like an useless operation. In the second example, all events are still properly ordered. In general, as long as counters go up, the algorithm works.

Another way of looking at correctness is trying to rebuild the total order manually. The hard requirement is that if an event A happens before an event B, then in the total order A will be placed before B. In both picture 2 and 3, everything is good.

Let's look into picture 2. Event (X) from second cell in P0 happens before the event (Y) of third cell of P1. To make sure X does come before Y in the total order it is required that the time of Y to be larger than X's. And it is. It doesn't matter if the time difference is 1 or 2 or 100.

in which the new values of an entry that corresponds to the receipt of a message is updated by adding 1 to the max of the entry before it in the same table and the timestamp of the received message, as shown below, which is quite different from what was performed in the first illustration

It's actually pretty much the same logic, with exception of incrementing local counter before taking max. Generally speaking, every process has its own clock and every event increases that clock by one. The only exception is when a clock of a different process is already in front, then taking max is required to make sure all events have correct total order. So, in the third picture, P2 adjusts clock (taking max) as P3 is way ahead. Same for P1 adjust.